Analytic solutions of a class of extended constrained matrix maximization problems

Wei-wei Xu, Zhi-hao Ge and Lei Zhu

Applied Mathematics and Computation, 2020, vol. 372, issue C

Abstract: In this paper we extend key Lemma 3.1 of Xu et al. (2018) and Theorem 3.5 of Xu et al. (2019) to more general cases and propose analytic solutions of the following extended constrained matrix maximization problems:maxUkUkH=In,VkVkH=Im|det(cIm+∏k=1sΓkUkΔkVk)|,maxUkUkH=In,VkVkH=Im|tr(cIm+∏k=1sΓkUkΔkVk)|,whereΓk=(ΓrkOr×(n−r)O(m−r)×rO(m−r)×(n−r))∈Cm×n,Δk=(ΔrkOr×(m−r)O(n−r)×rO(n−r)×(m−r))∈Cn×mwithΓrk=diag(γ1k,⋯,γrk),Δrk=diag(δ1k,⋯,δrk),r=min{m,n},γik,δik∈R,k=1,…,s;i=1,…,rand c is a complex number, Im denotes the m-order identity matrix, Γk, Δk are m × n and n × m complex matrices, γik,δik are real numbers, and det(·),tr(·) denote the matrix determinant and trace functions. This is a non-convex nonlinear constrained matrix maximization problem. The new results improve the corresponding existing ones in the above two references.

Keywords: Constrained matrix determinant maximization problems; Singular value; Determinant function (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300319309816
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:372:y:2020:i:c:s0096300319309816

DOI: 10.1016/j.amc.2019.124989

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().